\newproblem{lay:4_6_13}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.6.13}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	If $A$ is a $7\times 5$ matrix, what is the largest possible rank of $A$? If $A$ is a $5\times 7$ matrix, what is the largest possible rank of $A$? Explain your answers.
}{
  % Solution
	In both cases the rank can be 5 at maximum, because for any $m\times n$ matrix the rank meets (Rank Theorem)
	\begin{center}
		$\dim\{\mathrm{Row}\{A\}\}=\dim\{\mathrm{Col}\{A\}\}=\mathrm{Rank}\{A\}$
	\end{center}
	In the first case, the rank cannot be larger than 5 because there are only 5 columns. In the second case, the rank cannot be larger than 5 because
	there are only 5 rows.
}
\useproblem{lay:4_6_13}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
